(Python) How to add items in context menu in 2.8?
The Shader Editor context menu is called NODE_MT_context_menu (found by inspecting Preferences> Keymap> Node Editor and looking for Right Mouse) and we can 'append' (add) a draw function, which draws your menu item, into the existing menu. In the example below I have used the Node Editor's existing 'Duplicate' operator.

def draw_menu(self, context):
    layout = self.layout
    layout.separator()
    layout.operator("node.duplicate_move", text="My new context menu item")

def register():
    bpy.types.NODE_MT_context_menu.append(draw_menu)

def unregister():
    bpy.types.NODE_MT_context_menu.remove(draw_menu)


Explanation:


The draw_menu function deals with the UI that you want to add to the context menu (an operator) by using the bl_idname of your operator - in this case node.duplicate_move. 
The register function should contain, in addition to the code that registers your operator, the code to append that UI into the existing menu.
In the case of an add-on, the unregister function will remove the UI you added.


Note:


The separator() line is not required, but useful for keeping your UI separate from the existing one.
prepend can be used instead of append to add items to the top of the menu instead of the bottom.


Some more information about menus can be found in the 2.80 Python API documentation. A few examples of extending the existing UI can be found in the Python templates included with Blender via the Templates menu in the Text Editor header.